Wavelets for Partial Differential Equations

Abstract

The property of wavelet characterization of Sobolev and Besov spaces that we saw in the previous section is quite a powerful tool. In the next sections we will see how we can take advantage of such a property in the design of new efficient methods for the solution of PDEs. Let us assume from now on that we have a couple of multiresolution analyses V _j and $\tilde V_j$ satisfying all space and frequency localization assumptions of Section 2.2.